This article develops an axiom system to justify an additive representation for a preference relation ${\succsim}$ on the product ${\prod_{i=1}^{n}A_{i}}$ of extensive structures. The axiom system is basically similar to the n-component (n ≥ 3) additive conjoint structure, but the independence axiom is weakened in the system. That is, the axiom exclusively requires the independence of the order for each of single factors from fixed levels of the other factors. The introduction of a concatenation operation on each factor A i (...) makes it possible to yield a special type of restricted solvability, i.e., additive solvability and the usual cancellation on ${\prod_{i=1}^{n}A_{i}}$ . In addition, the assumption of continuity and completeness for A i implies a stronger type of solvability on A i . The additive solvability, cancellation, and stronger solvability axioms allow the weakened independence to be effective enough in constructing the additive representation. (shrink)

Aworkshop was held August 26–28, 2015, by the Earth- Life Science Institute (ELSI) Origins Network (EON, see Appendix I) at the Tokyo Institute of Technology. This meeting gathered a diverse group of around 40 scholars researching the origins of life (OoL) from various perspectives with the intent to find common ground, identify key questions and investigations for progress, and guide EON by suggesting a roadmap of activities. Specific challenges that the attendees were encouraged to address included the following: What key (...) questions, ideas, and investigations should the OoL research community address in the near and long term? How can this community better organize itself and prioritize its efforts? What roles can particular subfields play, and what can ELSI and EON do to facilitate research progress? (See also Appendix II.) The present document is a product of that workshop; a white paper that serves as a record of the discussion that took place and a guide and stimulus to the solution of the most urgent and important issues in the study of the OoL. This paper is not intended to be comprehensive or a balanced representation of the opinions of the entire OoL research community. It is intended to present a number of important position statements that contain many aspirational goals and suggestions as to how progress can be made in understanding the OoL. The key role played in the field by current societies and recurring meetings over the past many decades is fully acknowledged, including the International Society for the Study of the Origin of Life (ISSOL) and its official journal Origins of Life and Evolution of Biospheres, as well as the International Society for Artificial Life (ISAL). (shrink)